Quantum-mechanical parameter

Quantum mechanical calculations generally have only one carbon atom type, compared with the many types of carbon atoms associated with a molecular mechanics force field like AMBER. Therefore, the number of quantum mechanics parameters needed for all possible molecules is much smaller. In principle, very accurate quantum mechanical calculations need no parameters at all, except fundamental constants such as the speed of light, etc. 

A Brief Review of the QSAR Technique. Most of the 2D QSAR methods employ graph theoretic indices to characterize molecular structures, which have been extensively studied by Radic, Kier, and Hall [see 23]. Although these structural indices represent different aspects of the molecular structures, their physicochemical meaning is unclear. The successful applications of these topological indices combined with MLR analysis have been summarized recently. Similarly, the ADAPT system employs topological indices as well as other structural parameters (e.g., steric and quantum mechanical parameters) coupled with MLR method for QSAR analysis [24]. It has been extensively applied to QSAR/QSPR studies in analytical chemistry, toxicity analysis, and other biological activity prediction. On the other hand, parameters derived from various experiments through chemometric methods have also been used in the study of peptide QSAR, where partial least-squares (PLS) analysis has been employed [25]. 

Berger and Wolfe (1996) reported a correlation of hydrolysis data for 12 sulfonylurea herbicides. The use of bond strength or Hammett a constants was impossible because of the complex structures of the compounds. The hydrolysis pathways for this class of compounds are also more complex, but the use of quantum mechanical parameters provided the detailed structural information needed to develop a useful correlation. As a result of the many different functional groups, several reaction pathways are available depending on the substituents. Also, there is a complicating pH effect on the pathways and the kinetics of hydrolysis as shown by product studies. The 12 herbicides used in this study are listed in Table 13.4, and the pseudo first-order hydrolysis rate constants are given in Table 13.5. Figure 13.2 shows the basic structure of these compounds. 

Semi-empirical calculations of quantum-mechanical parameters such as free valence, 7T-electron density distribution or localization energy also predict that addition at the less substituted end of the double bond is favoured (Sato and Cvetanovic, 1959 Jennings and Cvetanovi6, 1961 Binks and Szwarc, 1958). However the calculations are not accurate enough to account satisfactorily for the differences found for pentene-2 and indeed the different treatments predict opposite effects. 

Fig.1 The molecular geometry of DHP analogues. This geometry was adopted by Gaudio et al. to calculate some quantum mechanical parameters, which they used in their QSAR study [16]. The 1,4-dihydropyridine ring is shown to have a boat-like conformation and the phenyl ring to be bound to it at a pseudoaxial position and approximately bisecting the pyridine ring. From [16]. 1994 John Wiley Sons, Inc., reprinted by permission...

Some quantum mechanical parameters were also foimd to be useful in accounting for the variance in calcium channel blocking activity of nifedipine analogues. For the same set of compounds as treated by Coburn et al. (Table 3), Gaudio et al. [16] had correlated the contractile response inhibition data as... 

De Boer and Lunbeck showed that the reduced surface tension can be expressed as a function of the reduced temperature and the quantum mechanical parameter ... 

Hermann et al. obtained good correlations between the relative substrate efficiencies of some acetophenones toward rabbit kidney reductase and selected quantum mechanical parameters (122). The substituent indices were derived from electron density calculations and energy dif-... 

The equations generated in this study would be useful only for the nonpolar column (SE-30) on which the data were measured. However, in a broader sense, the types of descriptors used should apply to any nonpolar stationary phase. On polar phases, dipolar interactions would be expected to be more important and more sophisticated electronic descriptors would be needed (e.g., CNDO or MNDO quantum mechanical parameters). 

Benigni, R. Cotta-Ramusino, M. Andreoli, C. Giuliani, A. Electrophilicity as measured by K. molecular determinants, relationship with other physical-chemical and quantum mechanical parameters, and ability to predict rodent carcinogenicity. Carcinogenesis 1992,13, 547-553. 

The classical case corresponds to the vanishing de Broglie wave length. Formula (18.1.2) permits to visualize quite easily the factors which determine quantum effects. For heavy particles A is small and we may n lect the quantum effects. Also an increase in the interaction parameter e lowers A. If we consider for example the rare gases, both factors work in the same direction because with increasing number of electrons there is an increase in the polarisability of the molecule and consequently of e. For this reason the value of A drops rapidly if we go from He to A (cf. Table 18.1.1). Table 18.1.1 gives the values of the quantum mechanical parameter a for some atoms and molecules. 

We shall now consider very briefly the quantitative inteipretation of the change of the thermod3mamic properties with the quantum mechanical parameter A. 

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